slide1 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Photon Relaxation PowerPoint Presentation
Download Presentation
Photon Relaxation

Loading in 2 Seconds...

play fullscreen
1 / 25

Photon Relaxation - PowerPoint PPT Presentation


  • 63 Views
  • Uploaded on

Photon Relaxation. Ben Spencer. Introduction. Photon relaxation is a contribution to the area of error minimization in photon density estimation:. Estimate error is the sum of bias and noise . Goal is to reduce noise without increasing apparent bias .

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Photon Relaxation' - lael


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide3

Introduction

Photon relaxation is a contribution to the area of error minimization in photon density estimation:

  • Estimate error is the sum of bias and noise.
  • Goal is to reduce noise without increasing apparent bias.
  • Problem often addressed at the kernel level with filters/intelligent bandwidth selection.
  • Photon relaxation is different in that it directly manipulates the underlying point dataset.
slide4

Background

Challenges facing kernel-based noise removal:

  • Tricky to preserve high-frequency detail – particularly at sub-kernel scales – while ensuring adequate smoothing; noise removal and bias are correlated.
  • Wide bandwidths required to effectively filter all-frequency noise - increases rendering cost.

Photon relaxation addresses both of these points. Salient features of caustics can be preserved on a fine scale while allowing noise removal on a broader scale due to diffusion.

Furthermore, the relaxed distribution allows the use of very low-bandwidth kernels.

slide5

Background

What causes noise?

Two factors:

  • Point discrepancy. Caused by stochastic processes (e.g. scattering) and photon decoherence (geometry) during the particle tracing step.
slide6

Background

What causes noise?

Two factors:

  • Point discrepancy. Caused by stochastic processes (e.g. scattering) and photon decoherence (geometry) during the particle tracing step.
  • Variance in photon flux. This can be caused by absorption, attenuation, dispersion through dielectric media, etc.
slide7

Photon Relaxation

Basic principles:

  • Use point repulsion to minimize local discrepancy.
slide8

Photon Relaxation

1. For each photon, i, gather K-nearest neighbours to i.

slide9

Photon Relaxation

1. For each photon, i, gather K-nearest neighbours to i.

2. Compute individual repulsive forces on ifrom members, j, of K.

slide10

Photon Relaxation

3. Apply mean of forces to position of i.

1. For each photon, i, gather K-nearest neighbours to i.

2. Compute individual repulsive forces on ifrom members, j, of K.

slide11

Photon Relaxation

Basic principles:

  • Use point repulsion to minimize local discrepancy.
slide12

Photon Relaxation

Basic principles:

  • Use point repulsion to minimize local discrepancy.
  • Aim to relax distribution so it exhibits a blue noise spectral signature and low angular anisotropy.
slide13

Photon Relaxation

Basic principles:

  • Use point repulsion to minimize local discrepancy.

Radially-averaged power spectrum

  • Aim to relax distribution so it exhibits a blue noise spectral signature and low angular anisotropy.

Angular anisotropy

slide14

Photon Relaxation

Basic principles:

  • Use point repulsion to minimize local discrepancy.
  • Aim to relax distribution so it exhibits a blue noise spectral signature and low angular anisotropy.
  • Use diffusion to homogenize flux between photons.
slide19

Feature Detection and Preservation

Relaxation removes noise effectively, but photon diffusion also degrades larger-scale features of the distribution.

Sample PDF

Stochastically-seeded photon distribution

Diffusion results in degraded reconstruction

slide21

Feature Detection and Preservation

?

After relaxation. High-frequency detail has been lost due to diffusion.

Can we do better?

Before relaxation

slide22

Feature Detection and Preservation

Feature detection aims to preserve these features by detecting and inhibiting motion in the direction of migration.

Photons migrate along direction of density derivative.

Feature detection constrains photons in the direction of migration (red = constrained).

Reconstructed distribution better preserves PDF.

Sample PDF

slide23

Feature Detection and Preservation

Relaxation with no constraints

Before relaxation

Relaxation with constraints